Question

Prove by method of induction, for all n ∈ N
2 + 4 + 6 + ... + 2n = n (n+1)

Answer 1

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Answer 2

Answer:

2 + 4 + 6 + ... + 2n = n (n+1)

Step-by-step explanation:

2 + 4 + 6 + ... + 2n = n (n+1)

p(1) = 2  =  1(1 + 1)  

=> 2 = 2

p(2) = 2 + 2*2  = 2*(2 + 1)

=> 2 + 4  = 2 * 3

=> 6 = 6

Let say

p(K)  = 2 + 4 + 6 + ... + 2k = K (K+1)

then

p(K + 1) = 2 + 4 + 6 + ... + 2k + 2(K + 1)

= K (K+1) + 2(K + 1)

= ( K + 1)(K + 2)

= RHS

Hence

2 + 4 + 6 + ... + 2n = n (n+1)